My Favorite Algorithm: Metropolis-Hastings

http://flynnmichael.com/2015/06/01/my-favorite-algorithm-metropolis-hastings/

by mjfl • 11 years ago

95 21 11 years ago

Matumio• 11 years ago

I like the build-up explanation in this chapter (Monte Carlo Methods) from MacKay's book: http://www.inference.phy.cam.ac.uk/mackay/itprnn/ps/356.384....

stellographer6• 11 years ago

Interesting choice...

Seems like genetic algorithms, particle swarms etc. would be more attractive choices since they solve the same problem and are inherently parallelizable while Metropolis Hastings is almost 100 years old and designed for a 4 function calculator.

Although I guess some people have meta-parallelized it... but still seems like a patch job compared to modern likelihood navigation algos.

enupten3• 11 years ago

One of the parallelized versions is Gibbs sampling that is used for sampling from Bayesian networks. In this case you don't even need a proposal distribution; neither would you need the test from MH.

I think Graphlab (https://dato.com/) comes implemented with something of this kind.

The trouble with Particle swarms/Genetic algorithms is that they aren't guaranteed to sample from the underlying p.d. It is not yet apparent whether you can find the mode of a distribution faster by choosing a Markov chain whose stationary distribution is different from the underlying one.

stellographer6• 11 years ago

Are you sure that Gibbs sampling isn't just the multivariate version of MH?

What I'm saying is that convergence speed for MH is limited by the fact that guesses cannot communicate with each other... which doesn't matter when you have a pencil and a 4 function calculator like when it was designed.

A genetic algorithm or a particle swarm algorithm is capable of much swifter convergence because the guesses _can_ communicate and influence the direction of the drunken walk.

murbard23• 11 years ago

No!

The point of Metropolis-Hastings is to sample from a distribution when you do not know the partition function. It is the most important building blocks in a set of algorithms broadly known as Markov Chain Monte Carlo. These algorithms are particularly useful when performing Bayesian statistics.

Genetic algorithms will not give you samples from a distribution, they only perform optimization. Particle swarms also focus on optimization, and on top of that, they do not seem to have either theoretical justification or empirical success.

MH is embarrassingly parallel since you run multiple chains at the same time. Again, the point isn't optimization (that would be simulated annealing) but sampling.

Being 100 years old is also largely irrelevant. People will publish new algorithms to get publications all the time. That do not mean they necessarily outperform the old ones. Gradient descent is the basic algorithm used in training all of these cool new deep learning algorithms, and it's much older than MH.

Yes, there are more recent improvements to MH, the two biggest ones being Hamiltonian Monte Carlo (which uses gradient information) and Parallel Tempering (which is somewhat similar to homotopy optimization), but that's hardly a reason to dismiss the importance of this algorithm.

stellographer6• 11 years ago

I see you feel strongly about this.

"The point of Metropolis-Hastings is to sample from a distribution when you do not know the partition function." That's one point, yes. The other is optimization. In which case I prefer the others I mentioned.

"they do not seem to have either theoretical justification or empirical success." That's just patently false. They _do_ have empirical success. And besides, a lot of these variants have MH implemented inside of them to some extent o.o

"MH is embarrassingly parallel since you run multiple chains at the same time." I can make six single grilled cheese sandwiches in 2 minutes, but it takes me 8 minutes to make a 6-decker grilled cheese. Is that a parallel process?

"Being 100 years old is also largely irrelevant." In my opinion it is relevant since computation can now be done in completely new ways than 100 years ago.

gfodor• 11 years ago

I always go back and forth on which of the two things are more amazing: the fact that we can accurately estimate the rendering equation in tractable time, or the fact that the universe manages to do it in real time.

eru• 11 years ago

The universe can take all the time it wants. You wouldn't notice.

xioxox• 11 years ago

In practice, there are some nicer algorithms for doing Markov Chain Monte Carlo, such as Goodman & Weare's Affine Invariant sampler, as implemented in http://dan.iel.fm/emcee/current/ . This algorithm has the advantage of not needing a proposal distribution.

mandelken• 11 years ago

Listen to Press on the naming of the algorithm, seems like Metropolis just put his name on the paper:

https://youtu.be/4gNpgSPal_8?t=938

mjfl• 11 years ago

This is true! It should be called the Rosenbluth-Hastings algorithm.

My Favorite Algorithm: Metropolis-Hastings

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